Question:
As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30 degree and 45 degree . If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships
Answer:
Let AB is the light house. So AB = 75
From triangle ABC,
tan 45 = AB/BC
=> 1 = 75/BC
=> BC = 75
Again from triangle ADC
tan30 = AB/BD
=> 1/√3 = AB/(BC + CD)
=> 1/√3 = 75/(75 + CD)
=> 1/√3 = 75/(75 + CD)
=> 75 + CD = 75√3
=> CD = 75√3 - 75
=> CD = 75(√3 - 1)
So the difference between ships is 75(√3 - 1) m
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